Pinhole diffraction traps

Atomic dipole traps in the diffraction pattern behind a circular aperture for neutral atom quantum computing

The diffraction pattern immediately behind a circular aperture contains localized bright and dark spots that constitute atom traps. Our calculations show that for a 25 micron diameter pinhole, laser intensities of ~100 W/cm2 and laser detunings of ~1,000-10,000 linewidths, trap depths of ~1 mK and trap frequency of ~10 kHz result, making these traps suitable candidates for single atom traps for neutral atom quantum computing. The details of our calculations and results are shown in PRA 73, 013409 (2006).

$Schematic of setup. Rectangular box labeled Laser, 780 nanometers. Red arrow towards the right inidicating laser beam, upright rectangle labeled pinhole (25 micrometers), small red rectangle labeled Diffraction pattern.$

$Plot of relative intensity versus radial (y-) direction and axial (z-) direction of the diffraction pattern behind the pinhole of the schematic above. Rainbow color scale from violet (zero) to red (four).$

Figure: Setup and intensity pattern for normal incidence, primary bright spot trap and dark spot trap marked

These traps can be scaled up to a large two-dimensional (2D) array of traps that can be individually addressed for single qubit gates. The inter-trap distance is determined by the distance between pinholes. In addition, two-qubit gates can be facilitated by bringing pairs of atoms together and apart controllably. To achieve this, two laser beams of opposite circular polarization incident on the pinhole array at an angle are used. Behind each pinhole, two atoms in two different magnetic substates are trapped, one in each laser beam. Due to the polarization dependence of the dipole trapping potential, the two atoms can be brought together and apart without the atoms tunneling between sites. For more details on these polarization dependent diffraction traps, see PRA 83, 023408(2011).

$Schematic of setup for movable diffraction traps. Coordinate system is x into the page, y upward for the radial directions, and z to the right for the axial direction. Two red arrows are incident on an upright rectangle labeled Aperture, indicating the pinhole, towards the right. The laser beams are coming from equal angles plus and minus theta below (sigma plus laser beam) and above (sigma minus laser beam) the z-axis, respectively. A red rectangle behind the pinhole is labeled Diffraction pattern.$

$Animation of two side-by-side image plots of the potential energy of the diffraction pattern behind a pinhole with the laser beam configuration from the schematic above. As the angle gamma is varied from zero to a maximum value, the top graph's trap site (localized minimum) moves up and back to center, and the bottom graph's trap sites moves down and back to center. The top graph is for a rubidium 87 atom in the hyperfine ground state F=2, m=2, and the bottom one is for F=2, m=-2. Color scale is rainbow with violet for potential energy zero and red for the maximum value.$

Figure: Trapping potential energy for 87 Rb atoms in states F=2, mF=+2 (top) and mF=-2 (bottom). Axes: y (microns) vs. z (microns).

We are continuing our computational exploration of the properties of these traps for different pinhole and laser beam configurations.

In addition, we are working towards demonstrating these diffraction traps experimentally. We have successfully constructed a magneto-optical atom trap (MOT). We are currently setting up equipment and developing LabVIEW codes to transfer atoms from the MOT to the diffraction traps. In order to place the diffraction traps into the MOT vacuum chamber without obstructing the optical access need for the MOT with the pinhole mask, we plan to project the pattern from immediately behind the pinhole into the chamber using a single lens. Changing the lens placement will allow us to create atom traps of different depths and sizes from the same diffraction pattern. Details of our calculations for the projection of the diffraction pattern can be found in PRA82, 063420 (2010).

$Two vertical lines with a gap of width a are labeled aperture. This location is labeled as zero. To the immediate right, inside a dotted region of interest, is the pinhole diffraction plot versus the radial and axial dimensions. This region is labeled one. A distance L to the right of this is the outline of a biconvex lens labeled as lens of focal length f. This location is labeled L. A distance z to the right of this is a dotted circle with another, smaller version of the diffraction pattern with the axial direction shortened extra relative to the radial direction. This is labeled optics-free region in vacuum chamber (MOT cloud). One point inside the circle is labeled example calculation point r comma z.$

Figure: Projection of diffraction pattern from immediately behind the pinhole into the MOT vacuum chamber.

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